F-theory vacua with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="double-struck">Z</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math> gauge symmetry

Cvetič, Mirjam; Donagi, Ron; Klevers, Denis; Piragua, Hernan; Poretschkin, Maximilian

doi:10.1016/j.nuclphysb.2015.07.011

Cited by 68 publications

(140 citation statements)

References 45 publications

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“…An obvious next step would be to apply the same reasoning also to genus-one fibrations with higher-degree multi-sections such as the trisection (Z 3 ) model studied in [9,13]. From a phenomenological point of view, discrete symmetries are known to be crucial ingredients in MSSM and GUT model building.…”

Section: Discussionmentioning

confidence: 99%

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Fluxes in F-theory compactifications on genus-one fibrations

Lin

Mayrhofer

Till

et al. 2016

J. High Energ. Phys.

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Abstract:We initiate the construction of gauge fluxes in F-theory compactifications on genus-one fibrations which only have a multi-section as opposed to a section. F-theory on such spaces gives rise to discrete gauge symmetries in the effective action. We generalize the transversality conditions on gauge fluxes known for elliptic fibrations by taking into account the properties of the available multi-section. We test these general conditions by constructing all vertical gauge fluxes in a bisection model with gauge group SU(5)×Z 2 . The non-abelian anomalies are shown to vanish. These flux solutions are dynamically related to fluxes on a fibration with gauge group SU(5)×U(1) by a conifold transition. Considerations of flux quantization reveal an arithmetic constraint on certain intersection numbers on the base which must necessarily be satisfied in a smooth geometry. Combined with the proposed transversality conditions on the fluxes these conditions are shown to imply cancellation of the discrete Z 2 gauge anomalies as required by general consistency considerations.

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Section: Discussionmentioning

confidence: 99%

“…This is a linear system of equations for the coefficients a i with a unique solution. This is because the Cartan matrices for the simple Lie algebras, which appear as intersection numbers in (2.12) through 13) are invertible. Here Θ is the divisor supporting non-abelian gauge symmetry in the base.…”

Section: Jhep01(2016)098mentioning

confidence: 99%

Fluxes in F-theory compactifications on genus-one fibrations

Lin

Mayrhofer

Till

et al. 2016

J. High Energ. Phys.

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“…F-theory compactifications that do not require the existence of a section are discussed e.g. in [36,51,[62][63][64][65][66][67][68]]. …”

Section: Jhep11(2017)081mentioning

confidence: 99%

Gauge backgrounds and zero-mode counting in F-theory

Bies

Mayrhofer²,

Weigand

2017

J. High Energ. Phys.

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Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.

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“…Finally, we describe briefly the possibility of systematic tunings of discrete abelian gauge factors. Such discrete factors, and corresponding matter, have been the subject of substantial recent work [72,[86][87][88][89][90][91][92][93]. As described in [72], one systematic way to approach discrete abelian factors is through the Higgsing of continuous abelian U(1) factors on states of higher charge.…”

Section: Discrete Abelian Gauge Factorsmentioning

confidence: 99%

“…resulting spectrum and Hodge shifts should be generic Z 2 : matter = (6n + 16 − 16g)(±1), (h 1,1 , h 2,1 ) = (0, −12n + 32(g − 1)). (8.4) A construction of a theory with a discrete abelian Z 3 symmetry from a U(1) factor with matter of charge q = ±3 was given in [91]. While constructions of models with more complicated groups and/or matter over generic bases have not been given explicitly in full generality, we can follow the same approach as used for the general U(1) k models to construct a class of potential Hodge numbers and spectra that should be a superset of the set of allowed F-theory possibilities.…”

Section: Original Papermentioning

confidence: 99%

Enhanced gauge symmetry in 6D F‐theory models and tuned elliptic Calabi‐Yau threefolds

Johnson

Taylor

2016

Fortschritte der Physik

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We systematically analyze the local combinations of gauge groups and matter that can arise in 6D F-theory models over a fixed base. We compare the low-energy constraints of anomaly cancellation to explicit F-theory constructions using Weierstrass and Tate forms, and identify some new local structures in the "swampland" of 6D supergravity and SCFT models that appear consistent from low-energy considerations but do not have known F-theory realizations. In particular, we classify and carry out a local analysis of all enhancements of the irreducible gauge and matter contributions from "non-Higgsable clusters," and on isolated curves and pairs of intersecting rational curves of arbitrary self-intersection. Such enhancements correspond physically to unHiggsings, and mathematically to tunings of the Weierstrass model of an elliptic CY threefold. We determine the shift in Hodge numbers of the elliptic threefold associated with each enhancement. We also consider local tunings on curves that have higher genus or intersect multiple other curves, codimension two tunings that give transitions in the F-theory matter content, tunings of abelian factors in the gauge group, and generalizations of the "E 8 " rule to include tunings and curves of self-intersection zero. These tools can be combined into an algorithm that in principle enables a finite and systematic classification of all elliptic CY threefolds and corresponding 6D F-theory SUGRA models over a given compact base (modulo some technical caveats in various special circumstances), and are also relevant to the classification of 6D SCFT's. To illustrate the utility of these results, we identify some large example classes of known CY threefolds in the Kreuzer-Skarke database as Weierstrass models over complex surface bases with specific simple tunings, and we survey the range of tunings possible over one specific base.arXiv:1605.08052v2 [hep-th]

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F-theory vacua with Z3 gauge symmetry

Cited by 68 publications

References 45 publications

Fluxes in F-theory compactifications on genus-one fibrations

Fluxes in F-theory compactifications on genus-one fibrations

Gauge backgrounds and zero-mode counting in F-theory

Enhanced gauge symmetry in 6D F‐theory models and tuned elliptic Calabi‐Yau threefolds

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